The present invention relates to a surface acoustic wave resonator.
A conventional surface acoustic wave resonator was proposed by Clinton Silvester Hartmann et al. (U.S. Pat. No. 3,886,504). FIG. 1 shows its basic structure. Interdigital transducer (to be referred to as IDT hereinafter) 2, as a converter between an electric signal and a surface acoustic wave, is arranged at the center of the surface of piezoelectric substrate 1. IDT 2 comprises a pair of comb-shaped transducers having a plurality of electrode fingers 4 arranged parallel to each other at equal distances, so that fingers 4 of the respective transducers are alternately arranged. Grating reflectors 3A and 3B are arranged on either side of IDT 2, and each has a plurality of reflective arrays 5 arranged parallel to each other at equal distances.
When an excitation signal is supplied to IDT 2, a surface acoustic wave that propagates to both sides of IDT 2 along the substrate surface, is produced. The surface acoustic wave is reflected by opposed reflectors 3A and 3B, thus causing resonance therebetween. Energy from the surface acoustic wave, caused by this resonance, is re-converted into electric energy by IDT 2.
Different structures of reflective arrays 5 of reflectors 3A and 3B, shown in sectional views of FIGS. 2A to 2C, are well known. FIG. 2A shows reflective arrays formed by thin film conductors 7 on LiNbO.sub.3 substrate 6. Reflection of a surface acoustic wave occurs since different portions of substrate 6 have different acoustic impedances depending upon the presence/absence of conductors 7.
When a reflective array comprises a thin film conductor, the reflectivity per reflective array is proportional to electromechanical coupling factor K.sup.2 of substrate 6. A Y-Z LiNbO.sub.3 substrate has a reflectivity of about 1.5%. However, reflective arrays with the above structure, arranged on a substrate with a small K.sup.2, cannot provide sufficient reflectivity. For this reason, as shown in FIG. 2B, reflective arrays can be grooves 9 in a surface of substrate 8, or, as shown in FIG. 2C, reflective arrays can be steps 11 of dielectrics or metals formed on a surface of substrate 10.
When IDT 2 and grating reflectors 3A and 3B are arranged at appropriate positions on substrate 1, a surface acoustic wave resonator allows for an operation electrically equivalent to a resonance circuit having high selectivity Q with reference to a signal output terminal of IDT 2.
In general, as shown in FIG. 1, when reflective arrays 5 of reflectors 3A and 3B are arranged at distances P, equal to half the wavelength of a resonating surface acoustic wave, surface acoustic waves reflected from arrays 5 have the same phase and are combined, resulting in maximum reflection. Distance between each two adjacent electrode fingers 4 of IDT 2 is designed to be equal to half of wavelength P of the surface acoustic wave. When reflectors 3A and 3B are arranged at distances equal to an integer multiple of P, the surface acoustic wave reflects repeatedly between reflectors 3A and 3B, and a steep standing wave is formed. More specifically, sides of reflective arrays 5, closer to IDT 2, are arranged at nodes of the surface acoustic standing wave. Each electrode finger 4 of IDT 2 is most preferably arranged at an antinode of the surface acoustic standing wave. For this reason, although electrode fingers 4 of IDT 2 and reflective arrays 5 of reflectors 3A and 3B are arranged at equal distances respectively, the distances between the electrode fingers 4 and the reflective arrays 5 are different from each other. Distance d between electrode finger 4 of IDT 2 closest to reflector 3A (or 3B) and reflective array 5 of reflector 3A (or 3B) closest to IDT 2 is set to be d=(N/2.+-.1/8).times..lambda., when a surface acoustic wave wavelength in resonance is given as .lambda. . Note that N is the natural number and the sign of the double sign is determined corresponding to the sign of the reflection coefficient determined by the reflector structure. In either sign, d is not equal to .lambda./2(=P).
One of the important factors in evaluating the performance of a surface acoustic wave resonator is the selectivity Q (to be referred to as "Q value" hereinafter). In general, a larger Q value is required for surface acoustic wave resonators applied to oscillators, resonance filters and the like. The Q value of a surface acoustic wave resonator is determined by losses occuring when the surface acoustic wave travelles between opposed grating reflectors. Such losses mainly include (1) propagation loss in the substrate itself, (2) external leakage loss from grating reflectors, (3) mode conversion loss from the surface acoustic wave mode to the bulk wave mode at final end portions (portions near the sides of the IDT) of grating reflectors, and the like. The loss of (1) is inherent in the crystal of the substrate and cannot be improved by designs of electrode fingers, reflective arrays or the like. The Q value determined only by the loss of (1), excluding losses of (2) and (3), is called a material Q value, and is an upper limit for the Q value.
In an actual surface acoustic wave resonator, since the losses of (2) and (3) are present, only a resonator having a Q value considerably below the material Q value can be achieved. In order to reduce the loss of (2), reflectivity of grating reflectors must be enhanced. To do this, the number of reflective arrays needs be increased, or, alternatively, reflectivity per reflective array must be enhanced. However, when the number of reflective arrays is increased, a large resonator is the inevitable result. Alternatively, an increase in resonator size can be avoided by increasing reflectivity per reflective array. However, in doing this, the mode conversion loss of (3) becomes larger in proportion to the square of the increased amount of reflectivity, resulting in a low Q value.
In order to provide a surface acoustic wave resonator with a high Q value, grating reflectors having high reflectivity and less mode conversion loss are needed. A reflector having a grooved structure in which the depth of the grooves is gradually changed, is described on pages 380 and 381 of Electronic Letters, Vol 13 No. 19 (Sept. 15th, 1977), by R. C. M. Li et al. as a reflector which can satisfy the above requirements. The grooves constituting reflective arrays of this grating reflector become deeper as they get further away from the IDT, and reflectivity thus gradually increases.
In general, if perturbation is infinitely repeated at a periodicity shorter than half the wavelength of a resonating surface acoustic wave in resonance, the bulk wave mode-converted from the surface acoustic wave is cancelled, and, as a result, formation of a radiation bulk wave does not occur. However, an actual resonator has a finite number of reflective arrays. In addition, the distance between the grating reflector and the IDT of a conventional resonator differs from that between the reflective arrays of the grating reflector and the electrode fingers of the IDT. Hence, a mode-converted bulk wave is radiated in the boundary portion between IDT 2 and grating reflectors 3A and 3B because it cannot be cancelled. In the method, in that portion of the grating reflectors near the IDT and where mode conversion occurs, the reflective array grooves can be made shallow, facilitating a corresponding lower reflectivity. In the inner portion of the grating reflectors where no radiation bulk wave is generated, the grooves can be made sufficiently deep so as to increase reflectivity. With this method, as has been stated, the Q value doubles. However, in order to form grooves whose depth gradually changes, a complex, manufacturing process which retards mass production, is sequired.
In recent years, improved surface acoustic wave resonators have been proposed in U.S. Pat. Nos. 4,454,488 (Hartmann) and 4,387,355 (Uno et al.).
In the former patent, an IDT is divided into first and second transducers, and a middle grating structure of reflective arrays is provided therebetween. The pitch between each two adjacent reflective arrays of grating reflectors and the pitch between those of the middle grating structure is set at different values, so that the surface acoustic wave propagates at the same speed in the IDT the grating reflectors and the middle grating structure. Thus, mode conversion loss is suppressed. In this prior art, the distance between two adjacent electrode fingers of the IDT is designed to be equal to half the wavelength of the surface wave (column 5, lines 65 to 66). For this reason, the electrode fingers of the IDT are shifted from the antinode of the standing wave, and the conversion efficiency of the IDT is decreased to about 80%.
The latter patent is characterized by the following points. The frequency at which the reflection factor of a reflector becomes maximum is made to coincide with the frequency at which radiation conductance of the IDT becomes maximum, in order to reduce resonance resistance. To achieve this the ratio of the distance between two adjacent electrode fingers to that between two adjacent reflective arrays is set to satisfy the resonance condition under the frequency conditions. In this prior art, the structures of the grating reflector and the IDT need not be the same. Therefore, the radiation bulk waves from the grating reflector and the IDT do not have the same intensity, and cannot be completely cancelled. For this reason, mode conversion loss cannot be suppressed.